I guess the customer is based in EU.
Supplies of goods to a customer registered for VAT in another EU country can be zero-rated provided certain conditions are met. These include obtaining the customer’s VAT registration number and showing it on the VAT invoice. The customer then accounts for VAT at the appropriate rate on the goods in the EU country of destination. If the conditions cannot be met, VAT must be charged in
the country of origin at the rate applicable to the goods in that country.
VAT must also be charged on supplies of goods to non-registered customers in other EU Member States. Where, however, the supplier is also responsible for the delivery of the goods, once the value of such ‘distance’ sales to any particular EU country exceeds an annual threshold set by that country, the supplier is automatically liable to register for VAT in that other country. VAT on any further sales is then due in the EU country of destination.
As long as you have verified that their EU VAT number is valid on the VIES system, and retain evidence that the goods physically left the UK then there is no issue with crediting and issuing a revised invoice.
The revised invoice should include a narrative referring to Article 138 of the EU VAT Directive.